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Journal of Lie Theory 24 (2014), No. 3, 889--908
Copyright Heldermann Verlag 2014

Symplectic Structures on Nilmanifolds: an Obstruction for their Existence

Viviana Del Barco
ECEN-FCEIA, Universidad Nacional de Rosario, Pellegrini 250, S2000BTP Rosario, Argentina

We introduce an obstruction for the existence of symplectic structures on nilpotent Lie algebras. Indeed, a necessary condition is presented in terms of the cohomology of the Lie algebra. Using this obstruction we obtain both positive and negative results on the existence of symplectic structures on a large family of nilpotent Lie algebras. Namely, the family of nilradicals of minimal parabolic subalgebras associated to the real split Lie algebra of classical complex simple Lie algebras.

Keywords: Symplectic structures, nilpotent Lie algebras, Lie algebra cohomolgy, minimal parabolic subalgebras.

MSC: 17B30, 17B56, 55T05, 53D05

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